Question

Write an exponential function y=ab^x for a graph that includes (1,15) and (0,6).
a. y=6(2.5)^x
b.y=3(5)^x
c.y=2.5(6)^x
d.y=5(3)^x

Answer 1

\[y=a b ^x\]
Use the points given to find a and b
So we have two equations:
\[15=ab^1 \text{ and } 6=ab^0\]

Answer 2

\[=>15=ab \text{ and } 6=a(1) \text{ since } b^0=1 \text{ assuming } b \neq 0\]

Answer 3

So if a=6 then what is b?

Answer 4

And actually you don't really need to know what b equals unless all of the answer choices are wrong lol

Answer 5

@myininaya

\geq
\[\geq\]
\leq
\[\leq\]
\Longrightarrow
\[\Longrightarrow\]

sorry to interrupt O_O

Answer 6

so it wud be a?

Answer 7

@CabDel do you know it is a or do you still have doubts it is a?

Answer 8

Well since u said A=6 im assuming thats the first number im sure it is.

Answer 9

and @kreshnik what is all of that for? What does it have to do with this question? I'm sorry

Answer 10

Do you understand how I got a=6?

Answer 11

Yes kind of.

Answer 12

I used the ordered pairs given:
\[(x_1,=1,y_1=15) \text{ and } (x_2=0,y_2=6)\]
And we have that we know the equation has this form:
\[y=ab^x\]

Answer 13

\[15=ab^1 \text{ and } 6=ab^0\]

Answer 14

I just replaced x with 1 and y with 15 for first ordered pair
then I replaced x with 0 and y with 6 for the second ordered pair
So I had two equations which I just wrote

Answer 15

\[15=ab \text{ and } 6=a\]

Answer 16

\[b^0=1 \text{ since } b \neq 0\]

Answer 17

=> 15=6b => 15/6=b
15/6 can be written as 2.5 because it is 2.5 lol
But yes the answer is a
but i just want you to be convinced that it is also a

Answer 18

Ok thanks im still trying to get used to this chapter its somewhat tough.

Answer 19

You can do it!
OpenStudy is here to help and root for ya!

Answer 20

Yeah hah thanks!. Anyway i gtg thanks for the help